publication . Article . 2009

accurate stationary densities with partitioned numerical methods for stochastic differential equations

Kevin Burrage; Grant Lythe;
Open Access
  • Published: 23 Apr 2009 Journal: SIAM Journal on Numerical Analysis, volume 47, pages 1,601-1,618 (issn: 0036-1429, eissn: 1095-7170, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
We devise explicit partitioned numerical methods for second-order-in-time scalar stochastic differential equations, using one Gaussian random variable per timestep. The construction proceeds by analysis of the stationary density in the case of constant-coefficient linear equations, imposing exact stationary statistics in the position variable and absence of correlation between position and velocity; the remaining error is in the velocity variable. A new two-stage “reverse leapfrog” method has good properties in the position variable and is symplectic in the limit of zero damping. Explicit new “Runge-Kutta leapfrog” methods are constructed, sharing the property t...
free text keywords: Numerical Analysis, Linear equation, Differential equation, Stationary distribution, Distribution function, Runge–Kutta methods, Random variable, Mathematical optimization, Mathematical analysis, Stochastic differential equation, Mathematics
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